I see some JavaScript scripts using »!0« and/or »!1« occasionally. What does that mean exactly?

Those are shortcuts for true and false, making use of JavaScript’s logical NOT operator (the exclamation point) and the fact that JavaScript uses weak typing, meaning that 0, false and null all mean the same in comparisons unless you force JavaScript to compare the type as well (by using ===). Using this knowledge, you can shorten true using !0 and false using !1.